University of Sydney Algebra Seminar

Mikhail Kotchetov (Memorial University of Newfoundland)

Friday 26th June, 12.05-12.55pm, Carslaw 375

Group gradings on finite-dimensional simple Lie algebras

Group gradings on algebras, especially simple algebras, have been extensively studied since the 1960s. In particular, gradings on Lie algebras arise in the theory of symmetric spaces, Kac-Moody algebras, and Lie coloralgebras. In the context of simple Lie algebras, it suffices to consider only gradings by abelian groups (since the support of any grading generates an abelian group). In 1968, V. Kac classified all gradings by cyclic groups on finite-dimensional simple Lie algebras. The study of gradings by arbitrary abelian groups on these algebras was started in the works by J. Patera and H. Zassenhaus in the late 1980s. We will discuss recent progress in this area.